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225The object of this report is to present a simple approximate solution for the stress concentration factor at the equator of, and parallel to the polar axis of, an oblately spheroidal cavity or crack subjected to a uniaxial stress acting at infinity and parallel to the polar axis. This and various related problems have been solved previously, with varying degrees of mathematical sophistication, by H. Neuber and J. H. Edwards [i], M. A. Sadowsky and E. Sternberg [2], and R. H. Edwards [3], but unfortunately the solutions are not readily accessible to the non-mathematician.For example, Sadowsky and Sternberg's solution is given in terms of Jacobian elliptic functions and although in principle a given required solution may be readily computed with the aid of available tables of Jacobian elliptic functions, Jacobi's zeta function, and complete elliptic integrals, this can be time consuming and also requires a thorough knowledge of the nomenclature used as well as a limited knowledge of the mathematical principles involved in the derivation of the original solution.The approximate solution for the particular stress concentration factor ~ under discussion here was found by following the approach of R. H. Edwards [3], and by approximating his expressions for one of the auxiliary position parameters and for the auxiliary harmonic function. The final expression, derived in this manner, takes the form = (~z)O / (~z) ~ = 4b/~a + 0.5 + where (az) is the tangential stress at the equator acting in the direction ~f the applied stress, i.e., parallel to the minor or polar axis of the cavity; (~)~ is the applied uniaxial stress acting at infinity; a and b are ~he semiminor and semimajor axes of the oblately spheroidal cavity, respectively (see Fig. I); and ~ is Poisson's ratio of the material.In order to compare this approximate solution with an accurate solution, that given by Neuber was computed for a range of shape ratios b/a and for various values of Poisson's ratio ~. The comparison is shown in Fig. 2. Fig. 3, which gives a further comparison of the two solutions, shows the sensitivity of ~ to Poisson's ratio for various shape ratios. Fig. 4 shows the relative error ratio between the approximate stress concentration factor ~ and the Neuber value a N as a function of shape ratio for various values of Poisson's ratio.It is seen that the Int Journ of Fracture 9 (1973)

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